Banquet Brango, Carlos AlbertoVillamizar Roa, Élder JesúsCorpa Liñan, Luis Enrique2022-09-012023-09-012022-09-012022-09-01https://repositorio.unicordoba.edu.co/handle/ucordoba/6508This thesis is devoted to the study of the initial value problem for a nonlinear plate equation in Rn × (0, ∞) with initial data in Modulation spaces, which includes the Bessel-potential Hs p and Besov B s p,q spaces, for large enought regularity index s. We derive a set of time-decay estimates for the corresponding linear plate equation on the framework of modulation spaces, and then, we use these results to analyze the existence and asymptotic stability of global solutions of the nonlinear problem.Declaración de Autoría ............................................................................................................................................................................................................................................. VResumen ......................................................................................................................................................................................................................................................................... VIIAgradecimientos ......................................................................................................................................................................................................................................................... XIINTRODUCCIÓN ............................................................................................................................................................................................................................................................. 11. PRELIMINARES .......................................................................................................................................................................................................................................................... 51.1. Lemas técnicos ........................................................................................................................................................................................................................................................ 51.2. Espacios $L^p$ ...................................................................................................................................................................................................................................................... 111.3. Transformada de Föurier ............................................................................................................................................................................................................................... 131.4. Espacio de Schwartz ........................................................................................................................................................................................................................................ 171.5. Transformada de Föurier en $L^2$ ....................................................................................................................................................................................................... 201.6. Distribuciones temperadas .......................................................................................................................................................................................................................... 211.7. Espacios de Sobolev ......................................................................................................................................................................................................................................... 241.8. Espacios de modulación .............................................................................................................................................................................................................................. 292. ESTIMATIVAS DE DECAIMIENTO ............................................................................................................................................................................................................... 392.1. Planteamiento del problema .................................................................................................................................................................................................................... 392.2. Estimativas de decaimiento en $L^{\infty}$ y $H^s_p$ ......................................................................................................................................................... 402.3. Estimativas de decaimiento en $M^s_{p,q}$ .................................................................................................................................................................................. 512.3.1. Estimativa de $\Vert \Lambda_{\theta,\frac{1}{2}}(t) g \Vert_{M^s_{p,q}}$ ................................................................................................................. 522.3.2. Estimativa de $\Vert \partial_t \Lambda_{\theta,1}(t) g \Vert_{M^{s-1}_{p,q}}$ ...................................................................................................... 572.3.3. Estimativa de $\Vert \partial_t S(t) u_0 \Vert_{M^{s}_{p,q}}$ ............................................................................................................................................ 602.3.4. Estimativa de $\Vert \partial_t^2 S(t) u_0 \Vert_{M^{s-1}_{p,q}}$ ................................................................................................................................... 632.3.5. Estimativa de $\Vert S(t) \Delta u_1 \Vert_{M^{s}_{p,q}}$ ..................................................................................................................................................... 662.3.6. Estimativa de $\Vert \partial_t S(t) \Delta u_1 \Vert_{M^{s-1}_{p,q}}$ ........................................................................................................................... 673. RESULTADOS DE EXISTENCIA ..................................................................................................................................................................................................................... 683.1. Espacios de solución ....................................................................................................................................................................................................................................... 683.2. Estimativas de no linealidad en espacios de Modulación .................................................................................................................................................... 683.3. Existencia de soluciones locales y globales en espacios de Modulación ................................................................................................................... 764. DISPERSIÓN Y ESTABILIDAD ASÍNTOTICA ........................................................................................................................................................................................ 835. CONCLUSIONES ................................................................................................................................................................................................................................................... 885.1. Conclusiones ......................................................................................................................................................................................................................................................... 885.2. Trabajos futuros ................................................................................................................................................................................................................................................. 88Bibliografía ..................................................................................................................................................................................................................................................................... 89application/pdfspaCopyright Universidad de Córdoba, 2022Trabajo de grado - Maestríainfo:eu-repo/semantics/embargoedAccessAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)Ecuación de placasEspacios de modulaciónEstimativas de decaimiento en tiempoSolución globalEstabilidadPlate equationsModulation spaces,Time-decay estimates,Global solutionsStability